This manuscript addresses trajectory tracking problem of autonomous underwater vehicles (AUVs) on the horizontal plane. Adaptive sliding mode control is employed in order to achieve a robust behavior against some uncertainty and ocean current disturbances, assuming that disturbance and its derivative are bounded by unknown boundary levels. The proposed approach is based on a dual layer adaptive...

Lokesh Vijayvargy,1 Pranay Goswami,2 and Bushra Malik3 1 Faculty of Management, Jaipuria Institute of Management, Jaipur 302033, India 2 Departement of Mathematics, Amity University Rajasthan, Jaipur 302002, India 3 Mathematics Department, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan Correspondence should be addressed to Pranay Goswami, [email protected] Receiv...

We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+T basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit. The equivalent T -count of the synthesized circuit is bounded by k C0 log2(1/ε) +E(n, k), where k is the number of distinct phases in the diagonal n-qubit uni...

In this paper the simple structure between some convex sets in the Banach space H introduced by Hornich is used to determine the extreme points of the families K(a) of convex functions of order ~ and V(k) of functions with bounded boundary rotation k ~. For close-to-convex functions of order {1,/3 ~ ]0, 1[, a partial result is given. The results for K(~) and V(k) agree with those that hold for ...

The logarithmic law of the wall loses part its predictive power in flows with system rotation. Previous work on topic mean flow scaling has mostly focused streamwise, spanwise, or wall-normal main objective this is to establish for wall-bounded small but arbitrarily directional Our approach as follows. First, we apply dimensional analysis Reynolds-averaged momentum equation. We show that when a...

The effects of a background uniform rotating magnetic field acting in a conducting fluid with a parallel flow are studied analytically. The stationary version with a transversal magnetic field is well known as generating Hartmann boundary layers. The Lorentz force includes now one term depending on the rotation speed and the distance to the boundary wall. As one intuitively expects, the rotatio...

We construct a smoothly bounded pseudoconvex domain whose boundary contains no complex analytic variety such that some boundary point admits no holomorphic peak function.

The classic Poisson formula giving an integral representation of bounded harmonic functions in the unit disk in terms of its boundary values has a long history (as it follows from its very name). Given a Markov operator P on a state space X one can easily deene harmonic functions as invariant functions of the operator P, but in order to speak about their boundary values one needs a boundary, be...